Question

b. Identify the type of relation between the figure number and the number of dots in a figurec. Tell whether this relation is a function . Yes or Nod. Explain your answer to part c and represent the relation with an algebraic expression

Answer 1

a) To write the figure number and the corresponding number of dots:

b) To identify the type of relation between the figure number and the number of dots in a figure:

For the first figure,

1+3+1=5

For the second figure,

`\begin{gathered} 1+3+3+1=1+3(2)+1 \\ =8 \end{gathered}`

For the third figure,

`\begin{gathered} 1+3+3+3+1=1+3(3)+1 \\ =11 \end{gathered}`

For the fourth figure,

`\begin{gathered} 1+3+3+3+3+1=1+3(4)+1 \\ =14 \end{gathered}`

c) To tell whether this relation is a function or not:

Yes, it is a function.

d) To explain part (c) and find the algebraic expression:

For every n ( figure number) value, there is a unique D (number of dots) value.

So, this relation represents the function.

Then, the algebraic expression is,

`D=2+3(n),\text{ where n is the natural numbers}`